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Hierarchical And Mixing Properties Of Static Complex Networks Emerging From Fluctuating Classical Random Graphs

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  • SUMIYOSHI ABE

    (Institute of Physics, University of Tsukuba, Ibaraki 305-8571, Japan)

  • STEFAN THURNER

    (Complex Systems Research Group, HNO, Medical University of Vienna, Währinger Gürtel 18-20, A-1090 Vienna, Austria)

Abstract

The Erdös–Rényi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to lead to a static complex network with an arbitrary connectivity distribution. In particular, a scale-free network with the hierarchical organization is constructed without assuming any knowledge about the global linking structure, in contrast to the preferential attachment rule for a growing network. The hierarchical and mixing properties of the static scale-free network thus constructed are studied. The present approach establishes a bridge between a scalar characterization of individual vertices and topology of an emerging complex network. The result may offer a clue for understanding the origin of a few abundance of connectivity distributions in a wide variety of static real-world networks.

Suggested Citation

  • Sumiyoshi Abe & Stefan Thurner, 2006. "Hierarchical And Mixing Properties Of Static Complex Networks Emerging From Fluctuating Classical Random Graphs," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 17(09), pages 1303-1311.
    • Handle: RePEc:wsi:ijmpcx:v:17:y:2006:i:09:n:s0129183106009837
    DOI: 10.1142/S0129183106009837
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    References listed on IDEAS

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    1. Dorogovtsev, S.N. & Mendes, J.F.F., 2003. "Evolution of Networks: From Biological Nets to the Internet and WWW," OUP Catalogue, Oxford University Press, number 9780198515906, Decembrie.
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